Problem: Simplify the expression. $(3q+1)(-4q+3)$
Answer: First distribute the ${3q+1}$ onto the ${-4q}$ and ${3}$ $ = {-4q}({3q+1}) + {3}({3q+1})$ Then distribute the ${-4q}.$ $ = ({-4q} \times {3q}) + ({-4q} \times {1}) + {3}({3q+1})$ $ = -12q^{2} - 4q + {3}({3q+1})$ Then distribute the ${3}$ $ = -12q^{2} - 4q + ({3} \times {3q}) + ({3} \times {1})$ $ = -12q^{2} - 4q + 9q + 3$ Finally, combine the $x$ terms. $ = -12q^{2} + 5q + 3$